Calculation Policy As adopted by all schools within the Bredon Moles cluster: Ashton First School Bredon Hancock’s Endowed First School Bredon Hill Middle.

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Calculation Policy As adopted by all schools within the Bredon Moles cluster: Ashton First School Bredon Hancock’s Endowed First School Bredon Hill Middle School Broadway First School Broadway St Mary’s Catholic School Cropthorne C of E First School Eckington C of E First School Elmley Castle C of E First School Overbury C of E First School Sedgeberrow C of E First School Supported by Nina Holden from Worcestershire County Council.

Calculation Policy This policy has been devised to give children a consistent and smooth progression of learning in calculations. The calculation policy is organised according to age stage expectations as set out in the National Curriculum 2014, however, it is vital that pupils are taught according to the stage that they are currently working at, being moved onto the next level or building their confidence by working at a lower age stage. It is important that any type of calculation is given a real life context or problem solving approach to enhance their understanding of the purpose of the calculation.

Subtraction – Year 1 Subtract from numbers up to 20.
Read, write and interpret number sentences with - and = signs. Subtraction – Year 1 Subtract from numbers up to 20. Children consolidate understanding of subtraction practically, showing subtraction on bead strings, using cubes etc and in familiar contexts. Children are introduced to more formal recording using number lines. Subtracting by taking away Count back in ones on a numbered number line to take away, with numbers up to 20: Finding the difference This will be introduced practically with the language ‘find the difference’ and ‘how many more?’ in a range of contexts Mental Subtraction Children should start recalling subtraction facts up to and within 10 and 20 and should be able to subtract zero. Key number skills for subtraction at Year 1: Given a number say one more or one less. Count to and over 100, forward and back, from any number. Represent and use subtraction facts to 20 and within 20. Subtract with one-digit and two-digit numbers to 20 including zero. Solve one step problems that involve addition and subtraction, using concrete objects (i.e. Bead string, objects, cubes) and pictures and missing number problems. Read and write numbers from 0 to 20 in numerals and words. 7 – 4 = 3 Key Vocabulary Equal to, take, take away, less, minus, subtract, leaves, difference, how many more / less, most, least, count back, how many left?

Subtraction – Year 2 Subtract with 2-digit numbers.
Subtract on a number line by counting back, aiming to develop mental subtraction skills and making links about the relationship between addition and subtraction. This strategy will be used for: * 2-digit numbers subtract units (e.g. 36 – 7) * 2-digit numbers subtract tens ( e.g. 48 – 30) * Subtracting pairs of 2-digit numbers (see below) Mental strategy subtract numbers close together by counting on: 42 – 38 = 4 children are taught to recognise that when numbers are close together it is more efficient to Key number skills for subtraction Year 2: count on the difference. Recognise the place value of each digit in a 2-digit number. Recall and use subtraction facts to 20 fluently and derive and use related facts up to 100. Subtract using concrete objects, pictorial representations, including a 2-digit number and units, a 2-digit number and tens and two 2-digit numbers. Show that subtraction cannot be done in any order. Read and write numbers to at least 100 in numerals and words. Solve simple addition and subtraction problems including measures, using concrete objects, pictorial representations and increasing confidence. Recognise and use inverse relationship between addition and subtraction, using this to check calculations and missing number problems. Key Vocabulary: equal to, take, take away, less, minus, subtract, leaves, difference between, how many more/less, most, least, count back, how many left, difference, count on, strategy, partition, tens, units.

Subtraction – Year 3 Subtracting with 2 and 3-digit numbers.
Step 1 – Introduce column subtraction where no exchanging is required. Step 2 – introduce exchanging through practical subtraction. Explore partitioning in different ways so they understand that when you exchange the value is the same 82 = = = etc. Emphasise the value hasn’t changed, we have just partitioned it in a different way. Step 3 – once secure with subtracting requiring one exchange extend to more than one exchange. Fractions Add and subtract fractions with the same denominator within one whole. Key vocabulary: Equal to, take, take away, less, minus, subtract, leaves, distance between, how many less, least, count back, difference, count on, partition, tens, hundreds, units, exchange, decrease, value, digit. Key number skills at Year 3: Subtract mentally a 3-digit number and ones, tens and hundreds. Estimate answers and use inverse operations to check. Solve problems including missing number problems. Find 10 or 100 more or less than a given number. Recognise the place-value of each digit in a 3-digit number. Read and write numbers up to 1000 in numerals and words. Practise mental subtraction strategies such as subtracting near multiples of 10 and adjusting and select most appropriate methods to subtract, explaining why.

Subtraction – Year 4 Subtract with 4-digit numbers.
Fractions Add and subtract fractions with the same denominator. Subtracting using the column subtraction method as introduced in Year 3 but moving towards more complex numbers and values. Reinforce exchanging. Give plenty of opportunities to apply this to money and measures. Key number skills for subtraction at Year 4: Subtract by counting on where numbers are close together or they are near to multiples of 10, 100 etc. Children select the most appropriate and efficient methods for given subtraction calculations. Estimate and use inverse operations to check answers. Solve addition and subtraction 2-step problems, choosing which operations and methods to use. Solve simple measure and money problems involving fractions and decimals to two decimal places. Find 100 more or less than a given number. Count backwards through zero, including negative numbers. Recognise place value of each digit in a 4-digit number. Round any number to the nearest 10, 100 and 1000. Solve number and practical problems involving subtraction. Key vocabulary: Equal to, take, take away, less, minus, subtract, leaves, how many fewer, less than, most, least, count back, difference, count on, strategy, partition, tens, units, exchange, decrease, hundreds, value, digit, inverse

Subtraction – Year 5 Subtract with at least 4-digit numbers.
Compact column subtraction with exchanging. Subtract with larger integers. Fractions Add and subtract fractions with the same denominator. Subtract with decimal values, including mixtures of integers and decimals, aligning the decimal point. Create lots of opportunities for subtracting and finding differences with money and measure. Key vocabulary: Equal to, take, take away, less, minus, subtract, leaves, how many fewer, less than, most, least, count back, difference, count on, strategy, partition, tens, units, exchange, decrease, hundreds, value, digit, inverse, tenths, hundredths, decimal point, decimal Key number skills for subtraction at Year 5: Subtract numbers mentally with increasingly large numbers. Use rounding and estimation to check answers to calculations and determine in a range of contexts levels of accuracy. Solve addition and subtraction multi-step problems in context, deciding which operations and methods to use. Read, write, order and compare numbers to at least 1 million and determine the value of each digit. Count forwards or backwards in steps of powers of 10 for any given number up to 1 million. Interpret negative numbers in context, counting forwards and backwards with positive and negative integers. Round any number up to 1 million to the nearest 10, 100, 1000, and

Subtraction – Year 6 Subtracting with increasingly large and more complex numbers and decimal values. Using the compact column method to subtract more complex integers. Fractions Add and subtract fractions with different denominators and mixed numbers. Using the compact column method to subtract money and measures, including decimals with different numbers of decimal places. Key vocabulary: Equal to, take, take away, less, minus, subtract, leaves, how many fewer, less than, most, least, count back, difference, count on, strategy, partition, tens, units, exchange, decrease, hundreds, value, digit, inverse, tenths, hundredths, decimal point, decimal. Key number skills for subtraction at Year 6: Solve addition and subtraction multi-step problems in context, deciding which operations and methods to use. Read, write, order and compare numbers up to 10 million and determine the value of each digit. Round any whole number to a required degree of accuracy. Use negative numbers in context and calculate intervals across zero. Children need to utilise and consider a range of mental subtraction strategies, jottings and written methods before choosing how to calculate.

Multiplication – Year 1 multiply with concrete objects, arrays and pictorial representations.
How many legs will 3 teddies have? There are 3 sweets in one bag. How many sweets are in 5 bags altogether? Give children experience of counting equal groups of objects in 2s, 5s and 10s.  Present practical problem solving activities involving counting equal sets or groups, as above. Key number skills for multiplication at Year 1: Count in multiples of 2, 5 and 10. Solve one-step problems involving multiplication, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher. Make connections between arrays, number patterns, and counting in twos, fives and tens. Begin to understand doubling using concrete objects and pictorial representations. Key vocabulary: groups of, times, array, altogether, multiply, count, repeated addition.

Division – Year 1 Group and share small quantities.
Using objects, diagrams and pictorial representations to solve problems involving both grouping and sharing. Give the children division problems in a familiar context e.g. There are 6 children on this table and there are 18 pieces of fruit to share between us. If we share them equally, how many will we get? Can they work it out and give a division statement? Pupils should: Use lots of practical apparatus, arrays and picture representations. Be taught the difference between grouping and sharing. Count in multiples of 2s, 5s and 10s. Find half of a group of objects by sharing into 2 equal groups. Fractions Recognise ½ and ¼ as equal parts of an object, shape or quantity. Key number skills needed for division at Year1: Solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations, arrays with the support of the teacher. Through grouping and sharing small quantities, pupils begin to understand division and finding simple fractions of objects, numbers and quantities. They make connections between arrays, number patterns, and counting in twos, fives and tens. Key vocabulary: Share, share equally, one each, two each, group, groups of, array, divide.:

Multiplication – Year 2 Multiply using arrays and repeated addition (using at least 2s, 5s and 10s).
Use repeated addition on a number line: Start from zero, make equal jumps to work out multiplication facts. Use arrays: Use arrays to help teach children to understand the commutative law of multiplication e.g. 5 x 3 = 15, 3 x 5 = 15, 15 = 3 x 5, 15 = 5 x 3. Also show the repeated addition 3 x 5 = = 15. Use practical apparatus: Key number skills for multiplication at Year 2: Count in steps of 2, 3 and 5 from zero, and in 10s from any number. Recall and use multiplication facts from the 2, 5 and 10 multiplication tables, including recognising odds and evens. Write and calculate number sentences using the x and = signs. Show that multiplication can be done in any order (commutative). Solve a range of problems involving multiplication, using concrete objects, arrays, repeated addition, mental methods, and multiplication facts. Pupils use a variety of language to discuss and describe multiplication. Use mental recall: children should begin to recall multiplication facts for 2, 5 and 10 times tables through practice in counting and understanding of the operation. Key vocabulary: groups of, times, array, altogether, multiply, count, multiplied by, repeated addition, column, row, commutative, sets of, equal groups, times, as big as, once, twice, three times

Division – Year 2 Group and share using the ÷ and = sign.
Use objects, arrays, diagrams, pictorial representations and grouping on a number line. Fractions Simple fractions. Recognise, find, name and write fractions. Make links to fractions, see National Curriculum. This represents 12 ÷ 3, posed as how many groups of 3 are in 12? Pupils should also show that 12 ÷ 4 = 3. Arrays: Know and understand sharing and grouping: 6 sweets shared between 2 people, how many do they each get? There are 6 sweets, how many people can have 2 sweets each? 3 x 1 3 x 2 3 x 3 3 x 4 Grouping using a number line: Group from zero in equal jumps of the divisor to find out how many groups of _ in _ ? Also use practical apparatus to reinforce understanding. Key number skills needed for division at Year 2: Count in steps of 2, 3, and 5 from 0. Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers. Calculate mathematical sentences for multiplication and division within the multiplication tables and write them using the x, ÷ and = signs. Show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot. Solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts. Key vocabulary: Share, share equally, one each, two each…, group, groups of, array, divide, divided by, divided into, division, grouping, number line, left, left over.

Multiplication – Year 3 Multiply 2-digits by a single digit number.
Introduce the grid method: To do this children must be able to: Partition numbers into tens and units. Multiply multiples of ten by a single digit (e.g. 20 x 4) using their knowledge of multiplication facts and place value. Recall and work out multiplication facts in the 2, 3, 4, 5, 8 and 10 times table. Work out multiplication facts using other mental strategies (e.g. commutative law, near multiples, doubling etc.) use repeated addition and arrays to support the children’s understanding. Approximate, Calculate, Check it mate! Key vocabulary: groups of, times, array, altogether, multiply, count, multiplied by, repeated addition, column, row, commutative, sets of, equal groups, times, as big as, once, twice, three times, partition, grid method, multiple, product, tens, units, value. Key number skills for multiplication at Year 3: Recall and use multiplication facts for the 2, 3, 4, 5, 8 and 10 multiplication tables, and multiply multiples of 10. Write and calculate number statements using the multiplication tables they know, including 2-digit x single-digit, drawing upon mental methods, and progressing to reliable written methods. Solve multiplication problems, including missing number problems. Develop mental strategies using commutativity and associativity law (e.g. 4 x 12 x 5 = 4 x 5 x 12 = 20 x 12 = 240) Solve simple problems in contexts, deciding which operations and methods to use. Develop efficient mental methods to solve a range of problems e.g. using commutativity (4 × 12 × 5 = 4 × 5 × 12 = 20 × 12 = 240) and for missing number problems _ x 5 = 20, 3 x _ = 18, 8 x _ = 32 .

Division – Year 3 Divide 2 digit numbers by a single digit.
Approximate, Calculate, Check it mate! Grouping on a number line: Fractions Tenths. Recognise, find and write fractions. Make links to fractions, see National Curriculum. Children continue to work out unknown division facts by grouping on a number line from zero. They are also now taught remainders. 1 x 3 2 x 3 3 x 3 4 x 3 Once children are secure with division by grouping on a number line short division for larger 2-digit numbers should be introduced. Remind children of correct place value. Once children demonstrate a full understanding of remainders and the short division method, they can then be taught how to carry the remainder onto the next digit. Key number skills needed for division at Year 3: Recall and use multiplication and division facts for the 2, 3, 4, 5, 8 and 10 multiplication tables (through doubling, connect the 2, 4 and 8s). Write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods. Solve problems, in contexts, and including missing number problems, involving multiplication and division. Pupils develop efficient mental methods, for example, using multiplication and division facts (e.g. using 3 × 2 = 6, 6 ÷ 3 = 2 and 2 = 6 ÷ 3) to derive related facts (30 × 2 = 60, so 60 ÷ 3 = 20 and 20 = 60 ÷ 3). Pupils develop reliable written methods for division, starting with calculations of 2-digit numbers by 1-digit numbers and progressing to the formal written method of short division. Key vocabulary: Share, share equally, one each, two each…, group, groups of, array, divide, divided by, divided into, division, grouping, number line, left, left over, inverse, short division, exchange, remainder, multiple.

Multiplication – Year 4 Multiply 2 and 3-digits by a single digit, using all multiplication tables up to 12 x 12. Approximate, Calculate, Check it mate! Encourage column Addition to add accurately. Step 1: Step 2: Introduce the expanded column multiplication method: When introducing the column method make comparisons to the grid method. Key vocabulary: groups of, times, array, altogether, multiply, count, multiplied by, repeated addition, column, row, commutative, sets of, equal groups, times, as big as, once, twice, three times, partition, grid method, multiple, product, tens, units, value, inverse. Key skills for multiplication at Year 4: Recall multiplication facts for all multiplication tables up to 12 x 12. Recognise place value of digits in up to 4-digit numbers . Use place value, known facts and derived facts to multiply mentally, e.g. multiply by 1, 10, 100, by 0, or to multiply 3 numbers. Use commutativity and other strategies mentally 3 x 6 = 6 x 3 , 2 x 6 x 5 = 10 x 6 , 39 x 7 = 30 x x 7. Solve problems with increasingly complex multiplication in a range of contexts. Count in multiples of 6, 7, 9, 25 and 1000. Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones).

Division – Year 4 Divide up to 3-digit numbers by a single digit.
Fractions Hundredths. Solve problems. Write decimal equivalents. Make links to fractions, see National Curriculum. Division – Year 4 Divide up to 3-digit numbers by a single digit. Continue to develop short division and reactivate learning from Year 3 looking at the short division methods. Real life contexts need to be used routinely to recognise the place of division and how to apply it to problems. Key number skills needed for division at Year 4: Recall multiplication and division facts for all numbers up to 12 x 12. Use place value, known and derived facts to multiply and divide mentally, including: multiplying and dividing by 10 and 100 and 1. Pupils practise to become fluent in the formal written method of short division with exact answers when dividing by a one-digit number. Pupils practise mental methods and extend this to three-digit numbers to derive facts, for example 200 × 3 = 600 so 600 ÷ 3 = 200. Pupils solve two-step problems in contexts, choosing the appropriate operation, working with increasingly harder numbers. This should include correspondence questions such as three cakes shared equally between 10 children. Approximate, Calculate, Check it mate! Pupils need to be secure with the process of short division and must understand how to calculate remainders. Pupils move onto dividing numbers with up to 3-digits by a single digit. When the answer for the first column is zero children could initially write a zero above to acknowledge its place. Key vocabulary: Share, share equally, one each, two each…, group, groups of, array, divide, divided by, divided into, division, grouping, number line, left, left over, inverse, short division, carry, remainder, multiple, divisible by, factor.

Multiplication – Year 5 Multiply up to 4-digits by 1 or 2-digits.
Approximate, Calculate, Check it mate! Short multiplication for multiplying by a single digit Children need to be taught to approximate first e.g. they would round 72 x 38 to 70 x 40 = 2800 to check the reasonableness of their answer. Introduce long multiplication for multiplying by 2-digits Key number skills for multiplication at Year 5: Identify multiples and factors, using knowledge of multiplication tables to 12x12. Solve problems where larger numbers are decomposed into their factors. Multiply and divide integers and decimals by 10, 100 and 1000. Recognise and use square and cube numbers and their notation. Solve problems involving combinations of operations, choosing and using calculations and methods appropriately. Make comparisons between the grid method and the short column multiplication method to see how the steps are related. Move to more complex numbers: Key vocabulary: groups of, times, array, altogether, multiply, count, multiplied by, repeated addition, column, row, commutative, sets of, equal groups, as big as, once, twice, three times, partition, grid method, multiple, product, tens, units, value, inverse, square, factor, integer, decimal, short/long multiplication, carry.

Make links to fractions, see National Curriculum.
Division – Year 5 Divide up to 4 digits by a single digit, including those with remainders. Approximate, Calculate, Check it mate! Fractions Improper fractions. Mixed numbers. Thousandths. Percentages. Make links to fractions, see National Curriculum. Key number skills for division at Year 5: Recall multiplication and division facts for all numbers up to 12 x 12 (as in Y4). Multiply and divide numbers mentally, drawing upon known facts. Identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers. Solve problems involving multiplication and division where larger numbers are decomposed into their factors. Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000. Use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers. Work out whether a number up to 100 is prime, and recall prime numbers to 19. Divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context Use multiplication and division as inverses. Interpret non-integer answers to division by expressing results in different ways according to the context, including with remainders, as fractions, as decimals or by rounding (e.g. 98 ÷ 4 = 24 r 2 = 24½ = 24.5  25). Solve problems involving combinations of all four operations, including understanding of the equals sign, and including division for scaling by different fractions and problems involving simple rates. Short division, including remainder answers: Now that pupils are introduced to examples that give rise to remainder answers, division needs to have a real life meaning context, where pupils consider the meaning of the remainder and how to express it, i.e. as a fraction, a decimal, or as a rounded number or value depending on the context of the problem. Key vocabulary: Share, share equally, one each, two each…, group, groups of, array, divide, divided by, divided into, division, grouping, number line, left, left over, inverse, short division, carry, remainder, multiple, divisible by, factor, quotient, prime number, prime factor, composite, number(non-prime).

Multiplication – Year 6 Multiply decimals up to 2 decimal places by a single digit.
Children will be able to: Use rounding and place value to make approximations before calculating and use these to check answers against.   Use short multiplication to multiply numbers with more than 4-digits by a single digit; to multiply money and measures, and to multiply decimals with up to 2 d.p. by a single digit.   Use long multiplication to multiply numbers with at least 4 digits by a 2 digit number. Key number skills for multiplication at Year 6: Recall multiplication facts for all times tables up to 12 x 12 (as Y4 and Y5). Multiply multi-digit numbers, up to 4-digit x 2-digit using long multiplication. Perform mental calculations with mixed operations and large numbers. Solve multi-step problems in a range of contexts, choosing appropriate combinations of operations and methods. Estimate answers using rounding and approximation and determine levels of accuracy. Round any integer to a required degree of accuracy. Approximate, Calculate, Check it mate! Key vocabulary: groups of, times, array, altogether, multiply, count, multiplied by, repeated addition, column, row, commutative, sets of, equal groups, as big as, once, twice, three times, partition, grid method, multiple, product, tens, units, value, inverse, square, factor, integer, decimal, short/long multiplication, carry. tenths, hundredths.

Approximate, Calculate, Check it mate! Division – Year 6 Divide at least 4 digits by both single-digit and 2-digit numbers (including decimal numbers and quantities). Short division for dividing by a single digit Key number skills for division at Year 6: Recall and use multiplication and division facts for all numbers to 12 x 12 for more complex calculations. Divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context. Use short division where appropriate. Perform mental calculations, including with mixed operations and large numbers. Identify common factors, common multiples and prime numbers. Solve problems involving all 4 operations. Use estimation to check answers to calculations and determine accuracy, in the context of a problem. Use written division methods in cases where the answer has up to two decimal places. Solve problems which require answers to be rounded to specified degrees of accuracy. Pupils should continue to use this method and consider the most appropriate way to express the remainder. In this example rather than expressing the remainder as r 1, a decimal point is added. Long division for dividing by 2-digits Fractions Simplify fractions. Order fractions. Associate division with fractions. Make links to fractions, see National Curriculum. If dividing by a 2-digit number use either long division or consider short division using single digit factors e.g. when dividing by 21 divide by 3 and then by 7. Pupils should be introduced to this method once they are secure with the above method using decimals. Support pupils by writing down the multiples of the numbers you are dividing by (pupils can then refer to this throughout the calculation). Key vocabulary: Share, share equally, one each, two each…, group, groups of, array, divide, divided by, divided into, division, grouping, number line, left, left over, inverse, short division, exchange, remainder, multiple, divisible by, factor, quotient, prime number, prime factor, composite, number(non-prime).

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